diff --git a/elementpath/xpath1/xpath1_parser.py b/elementpath/xpath1/xpath1_parser.py
index eb1159c7..98a05480 100644
--- a/elementpath/xpath1/xpath1_parser.py
+++ b/elementpath/xpath1/xpath1_parser.py
@@ -19,8 +19,8 @@
     xsd10_atomic_types, xsd11_atomic_types, ATOMIC_VALUES
 from ..xpath_context import XPathSchemaContext
 from ..tdop import Parser
-from ..namespaces import XSD_ANY_SIMPLE_TYPE, XML_NAMESPACE, XSD_NAMESPACE, \
-    XSD_UNTYPED_ATOMIC, get_namespace, get_expanded_name, split_expanded_name
+from ..namespaces import XSD_ANY_SIMPLE_TYPE, XSD_ANY_ATOMIC_TYPE, XML_NAMESPACE, \
+    XSD_NAMESPACE, XSD_UNTYPED_ATOMIC, get_namespace, get_expanded_name, split_expanded_name
 from ..schema_proxy import AbstractSchemaProxy
 from ..xpath_token import XPathToken
 from ..xpath_nodes import XPathNode, TypedElement, AttributeNode, TypedAttribute, \
@@ -175,7 +175,7 @@ def nud_(self):
             self.parser.advance('(')
             if nargs is None:
                 del self[:]
-                if self.parser.next_token.symbol == ')':
+                if self.parser.next_token.symbol in (')', '(end)'):
                     raise self.error(code, 'at least an argument is required')
                 while True:
                     self.append(self.parser.expression(5))
@@ -186,7 +186,9 @@ def nud_(self):
                 return self
             elif nargs == 0:
                 if self.parser.next_token.symbol != ')':
-                    raise self.error(code, '%s has no arguments' % str(self))
+                    if self.parser.next_token.symbol != '(end)':
+                        raise self.error(code, '%s has no arguments' % str(self))
+                    raise self.parser.next_token.wrong_syntax()
                 self.parser.advance()
                 return self
             elif isinstance(nargs, (tuple, list)):
@@ -196,7 +198,7 @@ def nud_(self):
 
             k = 0
             while k < min_args:
-                if self.parser.next_token.symbol == ')':
+                if self.parser.next_token.symbol in (')', '(end)'):
                     msg = 'Too few arguments: expected at least %s arguments' % min_args
                     raise self.wrong_nargs(msg if min_args > 1 else msg[:-1])
 
@@ -215,7 +217,7 @@ def nud_(self):
                 elif k == 0 and self.parser.next_token.symbol != ')':
                     self[k:] = self.parser.expression(5),
                 else:
-                    break
+                    break  # pragma: no cover
                 k += 1
 
             if self.parser.next_token.symbol == ',':
@@ -260,8 +262,12 @@ def is_instance(self, obj, type_qname):
         if get_namespace(type_qname) == XSD_NAMESPACE:
             if type_qname == XSD_UNTYPED_ATOMIC:
                 return isinstance(obj, UntypedAtomic)
+            elif type_qname == XSD_ANY_ATOMIC_TYPE:
+                return isinstance(obj, AnyAtomicType)
             elif type_qname == XSD_ANY_SIMPLE_TYPE:
-                return isinstance(obj, (AnyAtomicType, list))
+                return isinstance(obj, AnyAtomicType) or \
+                    isinstance(obj, list) and \
+                    all(isinstance(x, AnyAtomicType) for x in obj)
 
             try:
                 if self.xsd_version == '1.1':
@@ -271,7 +277,11 @@ def is_instance(self, obj, type_qname):
                 pass
 
         if self.schema is not None:
-            return self.schema.is_instance(obj, type_qname)
+            try:
+                return self.schema.is_instance(obj, type_qname)
+            except KeyError:
+                pass
+
         raise ElementPathKeyError("unknown type %r" % type_qname)
 
     def is_sequence_type(self, value):
diff --git a/tests/test_xpath1_parser.py b/tests/test_xpath1_parser.py
index 6498f003..aaf958c4 100644
--- a/tests/test_xpath1_parser.py
+++ b/tests/test_xpath1_parser.py
@@ -32,8 +32,14 @@
 except ImportError:
     lxml_etree = None
 
+try:
+    import xmlschema
+except ImportError:
+    xmlschema = None
+
 from elementpath import *
-from elementpath.namespaces import XSD_NAMESPACE, XPATH_FUNCTIONS_NAMESPACE
+from elementpath.namespaces import XSD_NAMESPACE, XPATH_FUNCTIONS_NAMESPACE, \
+    XSD_ANY_ATOMIC_TYPE, XSD_ANY_SIMPLE_TYPE, XSD_UNTYPED_ATOMIC
 
 try:
     from tests import xpath_test_class
@@ -242,6 +248,65 @@ def test_wrong_nargs(self):
         self.wrong_type("contains('XPath', 'XP', 20)")
         self.wrong_type("boolean(1, 5)")
 
+    def test_xsd_qname_method(self):
+        qname = self.parser.xsd_qname('string')
+        self.assertEqual(qname, 'xs:string')
+
+        parser = self.parser.__class__(namespaces={'xs': XSD_NAMESPACE})
+        parser.namespaces['xsd'] = parser.namespaces.pop('xs')
+        self.assertEqual(parser.xsd_qname('string'), 'xsd:string')
+
+        parser.namespaces.pop('xsd')
+        with self.assertRaises(NameError) as ctx:
+            parser.xsd_qname('string')
+        self.assertIn('XPST0081', str(ctx.exception))
+
+    def test_is_instance_method(self):
+        self.assertTrue(self.parser.is_instance(datatypes.UntypedAtomic(1),
+                                                XSD_UNTYPED_ATOMIC))
+        self.assertFalse(self.parser.is_instance(1, XSD_UNTYPED_ATOMIC))
+        self.assertTrue(self.parser.is_instance(1, XSD_ANY_ATOMIC_TYPE))
+        self.assertFalse(self.parser.is_instance([1], XSD_ANY_ATOMIC_TYPE))
+        self.assertTrue(self.parser.is_instance(1, XSD_ANY_SIMPLE_TYPE))
+        self.assertTrue(self.parser.is_instance([1], XSD_ANY_SIMPLE_TYPE))
+
+        self.assertTrue(self.parser.is_instance('foo', '{%s}string' % XSD_NAMESPACE))
+        self.assertFalse(self.parser.is_instance(1, '{%s}string' % XSD_NAMESPACE))
+        self.assertTrue(self.parser.is_instance(1.0, '{%s}double' % XSD_NAMESPACE))
+        self.assertFalse(self.parser.is_instance(1.0, '{%s}float' % XSD_NAMESPACE))
+
+        self.parser._xsd_version = '1.1'
+        try:
+            self.assertTrue(self.parser.is_instance(1.0, '{%s}double' % XSD_NAMESPACE))
+            self.assertFalse(self.parser.is_instance(1.0, '{%s}float' % XSD_NAMESPACE))
+        finally:
+            self.parser._xsd_version = '1.0'
+
+        with self.assertRaises(KeyError):
+            self.parser.is_instance('foo', '{%s}unknown' % XSD_NAMESPACE)
+
+        if xmlschema is not None and self.parser.version > '1.0':
+            schema = xmlschema.XMLSchema("""
+                <xs:schema xmlns:xs="http://www.w3.org/2001/XMLSchema">
+                  <xs:simpleType name="myInt">
+                    <xs:restriction base="xs:int"/>
+                  </xs:simpleType>
+                </xs:schema>""")
+
+            self.parser.schema = xmlschema.xpath.XMLSchemaProxy(schema)
+            try:
+                self.assertFalse(self.parser.is_instance(1.0, 'myInt'))
+                self.assertTrue(self.parser.is_instance(1, 'myInt'))
+                with self.assertRaises(KeyError):
+                    self.parser.is_instance(1.0, 'dType')
+            finally:
+                self.parser.schema = None
+
+    def test_check_variables_method(self):
+        self.assertIsNone(self.parser.check_variables(
+            {'values': [1, 2, -1], 'myaddress': 'info@example.com', 'word': ''}
+        ))
+
     # XPath expression tests
     def test_node_selection(self):
         root = self.etree.XML('<A><B1/><B2/><B3/><B2/></A>')
@@ -736,6 +801,9 @@ def test_boolean_functions(self):
         self.check_value("boolean('   ')", True)
         self.check_value("boolean('')", False)
 
+        self.wrong_type("true(1)", 'XPST0017', "'true' function has no arguments")
+        self.wrong_syntax("true(", 'unexpected end of source')
+
         if self.parser.version == '1.0':
             self.wrong_syntax("boolean(())")
         else:
diff --git a/tests/test_xpath2_parser.py b/tests/test_xpath2_parser.py
index e14c579e..9c6a7581 100644
--- a/tests/test_xpath2_parser.py
+++ b/tests/test_xpath2_parser.py
@@ -112,6 +112,7 @@ def test_is_sequence_type_method(self):
         self.assertTrue(self.parser.is_sequence_type('item()?'))
         self.assertTrue(self.parser.is_sequence_type('xs:untypedAtomic+'))
         self.assertFalse(self.parser.is_sequence_type(10))
+        self.assertFalse(self.parser.is_sequence_type(''))
         self.assertFalse(self.parser.is_sequence_type('empty-sequence()*'))
         self.assertFalse(self.parser.is_sequence_type('unknown'))
         self.assertFalse(self.parser.is_sequence_type('unknown?'))
@@ -151,7 +152,7 @@ def test_check_variables_method(self):
                          {'values': 'xs:decimal+', 'myaddress': 'xs:string', 'word': 'xs:string'})
 
         self.assertIsNone(self.parser.check_variables(
-            {'values': 1, 'myaddress': 'info@example.com', 'word': ''}
+            {'values': [1, 2, -1], 'myaddress': 'info@example.com', 'word': ''}
         ))
 
         with self.assertRaises(NameError) as ctx:
@@ -946,6 +947,8 @@ def test_get_atomic_value(self):
 
         token = self.parser.parse('true()')
 
+        self.assertEqual(self.parser.get_atomic_value('xs:int'), 1)
+        self.assertEqual(self.parser.get_atomic_value('xs:unknown'), UntypedAtomic('1'))
         self.assertEqual(self.parser.get_atomic_value(schema.elements['d'].type),
                          UntypedAtomic('1'))
 
@@ -960,6 +963,10 @@ def test_get_atomic_value(self):
             with self.assertRaises(AttributeError) as err:
                 self.parser.get_atomic_value(schema)
 
+            value = self.parser.get_atomic_value('unknown')
+            self.assertIsInstance(value, UntypedAtomic)
+            self.assertEqual(value, UntypedAtomic(value='1'))
+
             value = self.parser.get_atomic_value(schema.elements['a'].type)
             self.assertIsInstance(value, UntypedAtomic)
             self.assertEqual(value, UntypedAtomic(value='1'))